Expenses Worksheet by swj99471


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Flow Diagram for The inference about
    two populations and ANOVA
• To help identify the procedure to use in
  performing inference type analysis we need
  to ask a few questions, and pay attention to
  the answers.
• The next slide provides a flow diagram that
  helps you determine the proper procedure to


                  The Flow Diagram
                                         1. How many
                     2 Populations       2. Define the       3 Populations
                                         tested (in

         Yes         Paired        No                                Are there any
                  observations?                           Yes        characteristics     No
                                                                   common to groups
Define mD;                            Check                         of observations?
H0: mD = 0                           whether
                                                    Run a                              Run a Single
H1: mD >,<,  0                      s12 = s 22
                                                    randomized                         factor
                                     using the
                                                    block design                       ANOVA

                          Yes      s12 = s 22 ?

                  Run a t-test                    Run a t-test
                  for m1-m2                       for m1-m2 Use
                  with pooled                     S12 and S22 to
                  variance                        construct the
                  estimate (Sp2)                  t-statistic

         Review Problem # 1
One factor in low productivity is the amount of time
wasted by workers. Wasted time includes time spent
cleaning up mistakes, waiting for more material and
equipment, and performing any other activity not related to
production. In a project designed to examine the problem,
an operations management consultant took a survey of 200
workers in companies that were classified as successful (on
the basis of their latest annual profits) and another 200
workers from unsuccessful companies. The amount of time
(in hours) wasted during a standard 40-hour workweek was
recorded for each worker. These data are stored in columns
1 (successful companies) and 2 (unsuccessful companies)
in file “Productivity”.                                    3

• Do these data provide enough evidence at
  the 1% significance level to infer that the
  amount of time wasted in unsuccessful
  firms exceeds that of successful ones?
 • Estimate with 95% confidence how much
    more time is wasted in unsuccessful firms
            than in successful ones.



          Review problem # 2
• Ikarus, the Hungarian bus maker, has lost its
  important CIS market and is reported on the verge
  of collapse. The company is now trying a new
  engine in its buses and has gathered the random
  samples of miles-per-gallon figures for the old
  engine versus the new provided in file “Ikarus”.
   • Is there evidence that the new engine is more
              economical than the old one?

         Review Problem # 3
The president of a large company is in the process of
deciding whether to adopt a lunchtime exercise program.
The purpose of such programs is to improve the health of
workers and, in so doing, reduce medical expenses. To get
more information she instituted an exercise program for
the employees in one office. The president knows that
during the winter months medical expenses are relatively
high because of the incidence of colds and flu.
Consequently, she decides to record medical expenses for
the 12 months before the program and for 12 months after
the program. The "before" and "after" expenses (in
thousands of dollars) are compared on a month-to-month
basis and shown in file “Expenses”.                       6

• Do the data indicate that exercise programs
  reduce medical expenses? (Test with a =
  • Estimate with 95% confidence the mean
    savings produced by exercise programs.



         Review Problem # 4
                         uh ah.xls
A study performed by a Columbia University professor
(described in Report on Business, August 1991) counted
the number of times per minute professors from three
different departments said "uh" or "ah" during lectures to
fill gaps between words. The data derived from observing
100 minutes from each of the three departments are stored
in file “uh-ah” (Column 1 contains all the data for the
English department, column 2 stores the data for the
mathematics department, and column 3 stores the data for
the political science department.) If we assume that the
more frequent use of "uh” and "ah" results in more boring
lectures, can we conclude at the 5% significance level that
some departments' professors are more boring than others?

         Review Problem # 5
The friendly folks at the IRS are always looking for ways
to improve the wording and format of its tax return forms.
Three new forms have been developed recently. To
determine which, if any, are superior to the current form,
120 individuals were asked to participate in an experiment.
Each one of the three new forms, as well as the currently
used form, were filled out by 30 different people. The
amount of time (in minutes) taken by each person to
complete the task was recorded and stored in File “IRS”.
The sample means and standard deviations were computed
as follows.

   –   Form 1: mean = 90.17, standard deviation =31.49.
   –   Form 2: mean = 95.77, standard deviation = 30.01.
   –   Form 3: mean = 106.83, standard deviation = 30.47.
   –   Form 4: mean = 111.17, standard deviation 31.99
• What conclusion can be drawn from these data? (Use ? =.05)
• What are the required conditions for the test conducted
  above? Does it appear that the required conditions of the test
  are satisfied? IRS.xls
• Can you determine which one of the forms
  takes the shortest time to fill in? Use a = .05


         Review Problem # 6
Many North Americans suffer from high levels of
cholesterol, which can lead to heart attacks. For those with
very high levels (over 280), doctors prescribe drugs to
reduce cholesterol levels. A pharmaceutical company has
recently developed three such drugs. To determine if any
differences exist in their benefits, an experiment was
organized. The company selected 25 groups of three men,
each of whom had levels in excess of 280. In each group,
the men were matched according to age and weight. The
drugs were administered over a two-month period, and the
reduction in cholesterol was recorded. The data are stored
in the first three columns of file Cholesterol. Do these
results allow the company to conclude at the 5%
significance level that differences exist among the three
new drugs?                                                  11

           Review Problem # 7
Phonex provides call center services for many different companies.
One of four cities is being considered where a new call center is to be
established. Managers will have to be transferred to the new location,
and Phonex tries to find whether differences in housing prices exist
across the four competing cites. Having concerns about the large
variability among house prices due to house age and size, each house
observed was classified by age +size category, and its price then
recorded. See Phonex.xls.

–   At 5% significance level, is there evidence to conclude that on the
    average house prices differ among the four cities?
–   Is it necessary to match house by Age+Size in the three cities (Alpha =
–   Answer to the best of your ability: Which city is most preferred in terms
    of house prices?

          Review Problem # 8
GroBros., A regional grocery store chain, is considering to
upgrading to a new series of price scanners. Scanners sometimes
have errors, and GroBros. wants to evaluate the average levels
of such errors for 4 different types of scanners(the current one,
and three new ones). Thirty different shopping baskets were
defined (which differ in the number of items, and the types of
items included). Each basket was scanned four times (by each
scanner) and then item prices were determined by hand. The
number of scanning errors in each basket was recorded. See file

a.   State the hypothesis of interest for this test.
b.   At 1% significance level, is there a difference between the
     number of errors among the scanners?                       13

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